Geodesic
On cusps of caustics by reflection in two dimensional projective Finsler metrics
Theoretical and applied mechanics, Tome 52 (2025) no. 1, p. 75

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Given a projective Finsler metric in a convex domain in the projective plane, that is, a metric in which geodesics are straight lines, consider the respective Finsler billiard system. Choose a generic point inside the table and consider the billiard trajectories that start at this point and undergo $N$ reflection off the boundary. The envelope of the resulting 1-parameter family of straight lines is the $N$th caustic by reflection. We prove that, for every $N$, it has at least four cusps, generalizing a similar result for Euclidean metric, obtained recently jointly with G. Bor.
DOI : 10.2298/TAM250109004T
Classification : 78A05, 37C83, 53A04
Keywords: caustic, Finsler billiards, projective Finsler metrics 
Serge Tabachnikov. On cusps of caustics by reflection in two dimensional projective Finsler metrics. Theoretical and applied mechanics, Tome 52 (2025) no. 1, p. 75 . doi: 10.2298/TAM250109004T
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